Meshfree and finite element nodal integration methods

By Michael A. Puso, Jiun-Shyan Chen, Edward Zywicz, William Elmer. 2008

254 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3ccc626127909e802e153a36688d75d1636fd827

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Adaptive element-free Galerkin method applied to the limit analysis of plates (2010, methodology): “In the framework of meshfree methods, it is advantageous if the problem under consideration can be solved by evaluating quantities at the nodes only [26–32].”
Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems (2014, methodology): “The strain smoothing stabilized conforming nodal integration (SCNI) has been proposed [9,10] to ease the situation, where derivatives are not directly evaluated at nodes which avoids the instability, but still requires attention because of additional unstable modes which may become excited in certai”
Locking‐free continuum displacement finite elements with nodal integration (2008, methodology): “[16].”
Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons (2013, background): “Even though the patch test is met, nodal integration requires additional stabilization to prevent the presence of spurious modes [57].”
Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection (2013, background): “A similar issue also plagues meshless methods as they feature non-polynomial functions and remedies for revival of polynomial consistency have been explored for quite some time now [14, 30, 24].”
Consistent element‐free Galerkin method (2014, background): “[25] reported that SCNI still could result in oscillations near the domain boundary, and they introduced an additional term to further stabilize SCNI.”
A novel twice-interpolation finite element method for solid mechanics problems (2010, background): “However, resulted from the complex construction of the trial functions, meshfree methods have inherent shortcomings in the stability and efficiency of numerical integration [ 16 ].”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “…1994, 1995); (cid:129) MPS: moving particle semi-implicit (Koshizuka and Oka 1996); (cid:129) MQ: multiquadrics; (cid:129) M-SCNI: modified SCNI (Puso et al. 2008); (cid:129) M-SNNI: modified SNNI (Chen et al. 2007b); (cid:129) NEM: natural element method (Braun and Sambridge 1995; Sukumar and…”
An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics (2016, methodology): “A stabilized conforming nodal integration (SCNI) has been proposed [15, 23, 32] where derivatives are not directly evaluated at nodes, which circumvents the instability without the use of any derivatives or additional sampling points.”
Second‐order accurate derivatives and integration schemes for meshfree methods (2012, unknown): “[6] reported that SCNI still could present saw-tooth mode at the domain boundary, and a stabilization term with a tunable parameter is added to further stabilize SCNI.”
Assessment of smoothed point interpolation methods for elastic mechanics (2010, unknown): “[27, 28].”
An arbitrary order variationally consistent integration for Galerkin meshfree methods (2013, background): “More recently, it has been shown that SCNI generates nonzero low energy modes because of the loss of coercivity in the limit of discretization, and a correction has been proposed to enhance the stability [17, 18].”